Error detection and correction are important features of most modern electronic data communication systems, including wired and wireless telecommunication systems and data recording systems. Electronic communication systems, such as data recording systems, use a variety of error detection coding techniques to permit correction of bit errors in transmitted and recorded symbols that are written to and read from data recording media, also referred to as data storage media. For example, magnetic recording systems, such as tape drives or disk drives, read data from a magnetic medium with a read head and transmit the recovered data to a signal processor, such as a Viterbi detector. Magnetic recording systems typically include error detection coding and error correction to ensure accuracy of the detected data sequences.
Magnetic media, such as magnetic hard drives, magnetic diskettes, magnetic tapes, magnetic tape cartridges, and magnetic-optical disks, can be categorized as either longitudinal or perpendicular. In longitudinal media, magnetic anisotropy extends parallel to the plane of the medium. In other words, in longitudinal media, the magnetic orientation of individual magnetic domains is generally parallel to the surface of the medium. In perpendicular media, on the other hand, magnetic anisotropy is perpendicular to the plane of the medium. In particular, in perpendicular media, the magnetic orientation of individual magnetic domains is perpendicular to the medium surface. Perpendicular media generally allow for a much higher storage density than can be achieved in longitudinal media.
Error detection coding in a magnetic recording system may include a parity bit check. For example, the most significant error events in longitudinal media contain an odd number of erroneous bits. Therefore, the magnetic recording system may include a single parity bit check to detect the error events. However, in perpendicular media, the critical error events may take different forms, as the inter-symbol interference (“ISI”) characteristics are substantially different from those present in longitudinal media. Therefore, a single parity bit check may not be able to detect most of the error events in perpendicular media.